id author title date pages extension mime words sentence flesch summary cache txt cana-1620 CT. Nagaraj On Arithmetical Traits of Doubt Fuzzy T-Ideals beneath the Normalization is a T-Algebra 2024 6 .pdf application/pdf 1839 114 79 Theorem: 3.3 Let any 𝐷𝐹𝑇𝐼 αΏ» of ᾎ, we can generate the 𝑁𝐷𝐹𝑇𝐼 of ᾎ βŠ‚ αΏ». Proof: Let αΏ» be a 𝐷𝐹𝑇𝐼 of ᾎ. Define a 𝐷𝐹𝑆 αΏ»n of ᾎ as Ώ𝑛(Γ£) = αΏ»(Γ£) + Ώ𝑐(0), βˆ€Γ£ ∈ ᾎ. Let Γ£, Ι“ ∈ ᾎ (i) Ώ𝑛(0) = αΏ»(0) + Ώ𝑐(0) ≀ αΏ»(Γ£) + Ώ𝑐(0) = Ώ𝑛(Γ£) β‡’ Ώ𝑛(0) ≀ Ώ𝑛(Γ£) (ii) Ώ𝑛(Γ£ βˆ— Δ‰) = αΏ»((Γ£ βˆ— Ι“) βˆ— Δ‰) + Ώ𝑐(0) ≀ π‘šπ‘Žπ‘₯{αΏ»((Γ£ βˆ— Ι“) βˆ— Δ‰), αΏ»(Ι“)} + Ώ𝑐(0) = π‘šπ‘Žπ‘₯{[αΏ»((Γ£ βˆ— Ι“) βˆ— Δ‰) + Ώ𝑐(0)], [αΏ»(Ι“) + Ώ𝑐(0)]} = π‘šπ‘Žπ‘₯{Ώ𝑛((Γ£ βˆ— Ι“) βˆ— Δ‰), Ώ𝑛 (Ι“)} ⇒Ώ𝑛(Γ£ βˆ— Δ‰) ≀ π‘šπ‘Žπ‘₯{Ώ𝑛((Γ£ βˆ— Ι“) βˆ— Δ‰), Ώ𝑛 (Ι“)} Also Ώ𝑛(0) = αΏ»(0) + Ώ𝑐(0) = αΏ»(0) = 𝑓(αΏ» (0)) ≀ 𝑓(αΏ»(Γ£)) = Ώ𝑓(Γ£) β‡’ Ώ𝑓(0) ≀ Ώ𝑓(Γ£) (b) Ώ𝑓(Γ£ βˆ— Δ‰) = 𝑓(αΏ» (Γ£ βˆ— Δ‰)) ≀ 𝑓 {π‘šπ‘Žπ‘₯{αΏ»((Γ£ βˆ— Ι“) βˆ— Δ‰), αΏ»(Ι“)}} = π‘šπ‘Žπ‘₯{𝑓(αΏ»(Γ£ βˆ— Ι“) βˆ— Δ‰), 𝑓(αΏ»(Ι“))} = π‘šπ‘Žπ‘₯{Ώ𝑓((Γ£ βˆ— Ι“) βˆ— Δ‰), Ώ𝑓(Ι“)} cache/cana-1620.pdf txt/cana-1620.txt